Best Known (131−75, 131, s)-Nets in Base 9
(131−75, 131, 98)-Net over F9 — Constructive and digital
Digital (56, 131, 98)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (6, 43, 34)-net over F9, using
- net from sequence [i] based on digital (6, 33)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 6 and N(F) ≥ 34, using
- net from sequence [i] based on digital (6, 33)-sequence over F9, using
- digital (13, 88, 64)-net over F9, using
- net from sequence [i] based on digital (13, 63)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 13 and N(F) ≥ 64, using
- net from sequence [i] based on digital (13, 63)-sequence over F9, using
- digital (6, 43, 34)-net over F9, using
(131−75, 131, 182)-Net over F9 — Digital
Digital (56, 131, 182)-net over F9, using
- t-expansion [i] based on digital (50, 131, 182)-net over F9, using
- net from sequence [i] based on digital (50, 181)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 50 and N(F) ≥ 182, using
- net from sequence [i] based on digital (50, 181)-sequence over F9, using
(131−75, 131, 4103)-Net in Base 9 — Upper bound on s
There is no (56, 131, 4104)-net in base 9, because
- 1 times m-reduction [i] would yield (56, 130, 4104)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 11284 075256 218817 468599 571511 416762 338410 654226 939475 110973 389090 602723 578482 631407 605153 818525 993307 744541 324627 640896 746305 > 9130 [i]